Write the Fraction in Simplest Form (27 cube root of z^2)^(1/3)

${(27 \sqrt[3]{z^{2}})}^{\frac{1}{3}}$

Apply the product rule to $27 \sqrt[3]{z^{2}}$ .

$27^{\frac{1}{3}} {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{1}{3}} {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{3 (\frac{1}{3})} {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{1}{3})} {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$

Rewrite the expression.

$3^{1} {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$

Evaluate the exponent.

$3 {\sqrt[3]{z^{2}}}^{\frac{1}{3}}$